Before writing and understanding the concept of
steady flow energy equation for turbine and compressor, let us first brief here
steady flow energy equation and after that we will analyze the steady flow
energy equation for turbine and compressor.

Brief
introduction of steady flow energy equation

For steady flow process, net quantity of energy
contained within the system will never change with respect to time. Therefore according
to the principle of conservation of energy, we will have following statement
and energy equation for a steady flow process.

Net quantity of energy entering to the control
volume = Net quantity of energy leaving the control volume

Now
let us come to the point i.e. Steady flow energy equation for a turbine

Turbine is basically defined as one prime mover where thermal energy of the high pressure fluid will be converted in to mechanical energy in terms of rotation of turbine shaft. Mechanical energy developed by turbine will be finally converted in to electrical energy.

Turbine is also designated as mechanical device that will provide the work energy through the expansion of fluid.

Let us see here the following figure, where high
pressure fluid enters at inlet 1-1 and low pressure fluid leaves the turbine at
its outlet section i.e. 2-2.

Let turbine is well insulated and hence there will
no heat energy interaction between system and surrounding and therefore we can
say that Q =0.

When fluid flows through a turbine, change in
kinetic energy could be assumed as zero as velocity of fluid flow will be small
and we can neglect the small change in kinetic energy of the fluid. Therefore,
we will have ΔKE =0

We have also assumed here that change in potential
energy is zero or we can say that ΔPE =0

Let us implement above data that we have mentioned
above in steady flow energy equation for a steady flow process and we will have
following equation

W
= H1 – H2

We can also say that, work energy produced by the
turbine during the process will be the result of drop in enthalpy.

Now,
let us see steady flow energy equation for a compressor

Compressor is basically defined as one mechanical device which is used for increasing the pressure of fluid by securing the work energy from the surrounding. Work energy will be supplied to the system i.e. compressor from surrounding with the help of a rotating shaft.Let us see here the following figure of compressor,
where low pressure fluid enters at inlet1 and high pressure fluid leaves the
compressor at its outlet section i.e. 2.

We must note it here that for a compressor, work
will be done over the system by the surrounding and hence work energy will be
taken here with negative sign. Therefore by considering the same assumption
that we have made above, we will have following energy equation for an
adiabatic compressor as mentioned here.

H1
– (-W) = H2

W
= H2 – H1

Or we can say that work done on compressor by
surrounding during the process will provide the result of increment in
enthalpy.